Related papers: On Delisle's geographical projection
Whilst Paul de Casteljau is now famous for his fundamental algorithm of curve and surface approximation, little is known about his other findings. This article offers an insight into his results in geometry, algebra and number theory.…
The angle defect, which is the standard way to measure curvature at the vertices of polyhedral surfaces, goes back at least as far as Descartes. Although the angle defect has been widely studied, there does not appear to be in the…
We briefly review a few aspects of the development of differential geometry which may be considered as being influenced by Einstein's general relativity. We focus on how Einstein's quest for a complete geometrization of matter and…
The theme of this book chapter is to discuss algorithms for identifying and reconstructing groups and clusters of galaxies out of the general galaxy distribution. I review the progress of detection techniques through time, from the very…
This is an overview of the life and works of Pavel Florensky, an important and singular figure of the period rightly described as the \emph{Silver Age of Russian mathematics}, with a substantial overlap with the \emph{Silver Age of Russian…
While Kepler was still working in Graz during 1598, some letters to his mentor Michael Maestlin demonstrate his interest in astronomical clocks and machines. The first letter, dated January 6, 1598 contains a detailed description of a…
One of the mayor topics in astronomy at the beginning of the 19th century was the interpretation of the observations of the first asteroids. In 1810 Christian Ludwig Gerling at the age of twenty two came to G\"ottingen University to…
The location of objects on the celestial sphere is a fundamental measurement in astronomy, and the distribution of these objects within the Milky Way is important for understanding their evolution as well as the large scale structure of the…
The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of $L^2$ contexts where we make precise the interplay between the three sides of the question: (i)…
Spherical localisation is a technique whose history goes back to M.Gromov and V.Milman. It's counterpart, the Euclidean localisation is extensively studied and has been put to great use in various branches of mathematics. The purpose of…
In this brief essay we succinctly comment on the historical origin of Hilbert geometry. In particular, we give a summary of the letter in which David Hilbert informs his friend and colleague Felix Klein about his discovery of this geometry.…
In this paper we discuss, from a historical and philosophical point of view, a variation of the meaning of the five postulates in Euclidean Geometry and we make a short reference to D. Hilberts formalism. We examine, throughout the ages,…
Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
Euclid is a European Space Agency medium class mission selected for launch in 2019 within the Cosmic Vision 2015-2025 programme. The main goal of Euclid is to understand the origin of the accelerated expansion of the Universe. Euclid will…
The early Renaissance artist Albrecht Durer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and mathematical tools for their trade. In the…
Partial differential equations are central objects in the mathematical modeling of natural and social sciences (sound propagation, heat diffusion, thermodynamics, electromagnetism, elasticity, fluid dynamics, quantum mechanics, population…
Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. The present study demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and…
A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…